Pulse Amplitude
Modulation

Cuthbert Nyack
This type of modulation is used as the first step in converting an
analog signal to a discrete signal or in cases where it may be
difficult to change the frequency or phase of the carrier.
In this case the carrier is a pulse train rather than a sine
wave and the spectrum of the carrier consists of several components
around nwc =
2np/T where T is the time between pulses.
The spectrum also contains a component at the modulating frequency
which may be used to recover the modulating signal. Unipolar PAM
also has an average value at w = 0.
The applet below shows some aspects of PAM signals.
Different
cases can be seen by varying Fn which is set by scrollbar '0'.
Fn = 0 shows the modulating signal, the carrier and the PAM.
Fn = 1 Shows the Frequency spectrum for unipolar PAM which has an
average value at 0 frequency.
Fn = 2 Shows the Frequency spectrum for bipolar PAM which does not
have a component at 0 frequency.
Fn = 3 shows the PAM signal reconstructed from the spectrum. The
spectrum often quoted for PAM is obtained by multiplying a pulse
sequence by a modulating signal. This produces a pulse sequence
whose amplitude follows the modulating signal as shown by Fn = 4.
In practice it is more convenient to have a constant amplitude
pulse sequence. Fn = 5 shows that the accuracy of the spectral
representation increases as the pulse width is reduced.

Fn = 6 shows the signal which results if the PAM is passed through
an ideal LP filter whose BW is set by ns and phase at cut off is set by
ff.
Fn = 7 and 8 shows the PAM and its spectrum when the modulating signal
is a triangular and modified triangular waveform respectively.
Fn = 9 and 10 shows what happens when the PAM is passed through
an RC circuit with time constant
t1.
Fn = 11, 12 and 13 shows that the output from the RC circuit
with time constant t2 is improved
if the value of the pulse is sampled and held until the next
pulse arrives.
PAM is used as the first step to produce a PCM signal.
Fn = 14 shows the PAM being quantized and the resulting
quantization noise. The number of bits is set by Nb and
shows that the quantization noise reduces as Nb is increased.
Fn = 15 and 16 show special cases of Fn = 14 with 3 and 6 bit
quantization respectively.
PAM allows several signals to be transmitted across a channel
using Time Division Multeplexing(TDM). Fn = 17 shows what is meant
by TDM. 2 PAM signals shown as red and yellow with modulating
signals shown as orange and pink are combined to form the
green signal which is then transmitted.